Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 780 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.If a + b = 17 and ab = 72, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 63 × 57.
3. 3.Use (a + b)(a − b) = a² − b² to find 55 × 45.
4. 4.Find the value of x² − 2xy + y² when x = 13 and y = 3.
5. 5.If a + b = 13 and ab = 22, what is a² + b²?
6. 6.Find the value of x² − y² when x = 12 and y = 1.
7. 7.If a + b = 15 and ab = 36, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 15².
9. 9.Use (a + b)² = a² + 2ab + b² to find 76².
10. 10.Use (a + b)(a − b) = a² − b² to find 99 × 81.
11. 11.Use (a − b)² = a² − 2ab + b² to find 15².
12. 12.Use (a + b)(a − b) = a² − b² to find 51 × 49.
13. 13.Use (a + b)² = a² + 2ab + b² to find 11².
14. 14.Use (a + b)² = a² + 2ab + b² to find 43².
15. 15.Find the value of x² + 2xy + y² when x = 14 and y = 11.
16. 16.Use (a + b)² = a² + 2ab + b² to find 95².
17. 17.Use (a − b)² = a² − 2ab + b² to find 35².
18. 18.Use a² − b² = (a + b)(a − b) to find 97² − 52².
19. 19.Use a² − b² = (a + b)(a − b) to find 33² − 12².
20. 20.Use (a + b)² = a² + 2ab + b² to find 92².
21. 21.Find the value of x² − 2xy + y² when x = 15 and y = 1.
22. 22.Use (a + b)² = a² + 2ab + b² to find 86².
23. 23.Use (a + b)² = a² + 2ab + b² to find 98².
24. 24.If a + b = 9 and ab = 18, what is a² + b²?
25. 25.If a + b = 21 and ab = 110, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 78².
27. 27.If a + b = 11 and ab = 18, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 54 × 46.
29. 29.Find the value of x² − y² when x = 7 and y = 1.
30. 30.Use (a + b)(a − b) = a² − b² to find 39 × 21.
31. 31.Use a² − b² = (a + b)(a − b) to find 28² − 17².
32. 32.Use (a + b)(a − b) = a² − b² to find 72 × 68.
33. 33.Use a² − b² = (a + b)(a − b) to find 20² − 12².
34. 34.Use a² − b² = (a + b)(a − b) to find 81² − 32².
35. 35.Use a² − b² = (a + b)(a − b) to find 87² − 71².
36. 36.Use (a − b)² = a² − 2ab + b² to find 37².
37. 37.Use (a − b)² = a² − 2ab + b² to find 32².
38. 38.Use a² − b² = (a + b)(a − b) to find 57² − 27².
39. 39.If a + b = 9 and ab = 8, what is a² + b²?
40. 40.If a + b = 12 and ab = 32, what is a² + b²?

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